Lemma 4 (Khinchin-Kahane inequality) [1]}
\(\forall n \in \mathbb {N}\) , let \(\sigma _1, \cdots , \sigma _n\)  be a family of i.i.d. Rademacher variables. Then for any \(1<p<q<\infty \) , we have:
\(\bigg (\operatornamewithlimits{\mathbb {E}}_{\sigma } \left[\big |\sum _{i=1}^n\sigma _if_i\big |^q\right]\bigg )^{{1}{q}} \le \left(\frac{q-1}{p-1}\right)^{{1}{2}} \cdot \bigg (\operatornamewithlimits{\mathbb {E}}_{\sigma } \left[\big |\sum _{i=1}^n\sigma _if_i\big |^p\right]\bigg )^{{1}{p}}.\) 

